Relative Velocity of locus of curves

In summary, the relative velocity of a locus of curves is the rate of change of the position of a point on a curve with respect to another moving curve. It differs from absolute velocity, which considers the motion of a point with respect to a fixed frame of reference. This concept is commonly used in navigation and tracking systems to determine the relative position and speed of moving objects. It can be negative, indicating two curves are moving in opposite directions. The formula for calculating relative velocity of locus of curves is vrel = d(r1-r2)/dt, where r1 and r2 are the position vectors of the two curves.
  • #1
bugatti79
794
1
Hi Folks,
I am struggling to see how eqn 4.1.17 is arrived at using using eqn 4.1.10 at bottom of attachment. Its not clear to me what [tex]\frac{d \phi}{dt}[/tex] is...apart from what is given in eqn 2.1.30...
Any ideas?
Thanks
Relative Velocity.png
 
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  • #2
I have an idea ... post a pic that can be read
 
  • #3
Hi.
Ok..I will try another picture again tomorrow.

I think there should be enough resolution in the photo when you zoom in.
Thanks
 
  • #4
Hi,

This is the best I can do regarding a readable picture where I have pasted the relevant eqns.

Relative Velocity r2.png

Thanks
 

Related to Relative Velocity of locus of curves

1. What is the definition of relative velocity of locus of curves?

The relative velocity of a locus of curves is the rate of change of the position of a point on a curve with respect to another moving curve.

2. How is relative velocity of locus of curves different from absolute velocity?

Absolute velocity refers to the rate of change of the position of a point with respect to a fixed frame of reference, while relative velocity of locus of curves considers the motion of one curve with respect to another.

3. What are some real-world applications of relative velocity of locus of curves?

Relative velocity of locus of curves is commonly used in navigation and tracking systems, such as in airplanes and satellites, to determine the relative position and speed of moving objects.

4. Can relative velocity of locus of curves be negative?

Yes, relative velocity of locus of curves can be negative. This indicates that the two curves are moving in opposite directions, resulting in a decrease in the distance between them.

5. How is relative velocity of locus of curves calculated?

The relative velocity of locus of curves can be calculated using the derivative of the position vectors of the two curves with respect to time. This can be represented by the formula vrel = d(r1-r2)/dt, where r1 and r2 are the position vectors of the two curves.

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